Geodesic
Analyticity and theorems of Liouville and Phragmén–Lindelöf type for general elliptic systems of differential equations
Sbornik. Mathematics, Tome 24 (1974) no. 1, pp. 127-143 
O. A. Oleinik; E. V. Radkevich. Analyticity and theorems of Liouville and Phragmén–Lindelöf type for general elliptic systems of differential equations. Sbornik. Mathematics, Tome 24 (1974) no. 1, pp. 127-143. http://geodesic.mathdoc.fr/item/SM_1974_24_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Certain theorems on the analyticity of solutions of elliptic equations are used to prove theorems on the behavior of solutions of general elliptic systems of differential equations in unbounded regions, analogous to the classical theorems of Liouville and Phragmén–Lindelöf for harmonic functions. Theorems on the uniqueness of the solutions for elliptic boundary-value problems are also proved. Bibliography: 9 titles.

[1] O. A. Oleinik, E. V. Radkevich, “O povedenii na beskonechnosti reshenii nekotorykh sistem uravnenii s chastnymi proizvodnymi”, Uspekhi matem. nauk, XXVIII:5 (173) (1973), 249–250 | MR

[2] E. M. Landis, “O povedenii reshenii ellipticheskikh uravnenii v neogranichennykh oblastyakh”, Trudy Mosk. matem. ob-va, XXXI (1974), 35–58 | MR

[3] Lax P. D., “A Phragmén-Lindelöf theorem in harmonic analysis and its application in the theory of elliptic equations”, Comm. Pure Appl. Math., 10:3 (1957), 361–389 | DOI | MR | Zbl

[4] M. A. Shifrin, “Teoremy liuvillevskogo tipa dlya ellipticheskikh uravnenii vysokogo poryadka”, Trudy Mosk. matem. ob-va, XXXIII (1975) | MR | Zbl

[5] A. Douglis, L. Nirenberg, “Interior estimates for elliptic systems of partial differential equations”, Comm. Pure Appl. Math., 8:4 (1965), 503–538 | DOI | MR

[6] S. Agmon, A. Duglis, L. Nirenberg, Otsenki reshenii ellipticheskikh uravnenii vblizi granitsy, IL, Moskva, 1962

[7] S. Agmon, A. Douglis, L. Nirenberg, “Estimates near the boundary for solutions of elliptic partical differential equations satisfying general boundary conditions, II”, Comm. Pure Appl. Math., 17:1 (1964), 35–92 | DOI | MR | Zbl

[8] S. Agmon, “On kernels eigenvalues and eigenfunctions of operators related to elliptic problems”, Comm. Pure Appl. Math., 18:4 (1965), 627–663 | DOI | MR | Zbl

[9] M. S. Agranovich, M. I. Vishik, “Ellipticheskie zadachi s parametrom i parabolicheskie zadachi obschego vida”, Uspekhi matem. nauk, XIX:3 (117) (1964), 53–161